Problem: Christopher is 4 times as old as Emily and is also 12 years older than Emily. How old is Emily?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Emily. Let Christopher's current age be $c$ and Emily's current age be $e$ $c = 4e$ $c = e + 12$ Now we have two independent equations, and we can solve for our two unknowns. Since we are looking for $e$ , and both of our equations have $c$ alone on one side, this is a convenient time to use elimination. Subtracting the second equation from the first equation, we get: $0 =$ $4e$ $-$ $ (e + 12)$ which combines the information about $e$ from both of our original equations. Solving for $e$ , we get: $3 e = 12$ $e = 4$.